|x-4| <3
=>. x-4<3 or -(x-4)<3
=>. x-4<3 or x+4>3
=>. x<7 or x>1
So solution is x>1 & x<7. =x€(1,7)
Hope it helps...
Regards,
Leukonov/Olegion.
The solution to the given inequality is:
[tex]1<x<7[/tex] i.e. in the interval form it is given by: (1,7)
Step-by-step explanation:We are given a inequality in term of variable x as follows:
[tex]|x-4|<3[/tex]
Now, we know that any inequality with modulus function is opened as follows:
If
[tex]|x-a|<b[/tex]
Then we have:
[tex]-b<x-a<b[/tex]
i.e. we may write it as:
[tex]a-b<x<a+b[/tex]
Here in the given expression we have:
a=4 and b=3
Hence, the solution is given by:
[tex]4-3<x<4+3\\\\i.e.\\\\1<x<7[/tex]
How many hours are there in 1 week, 3 and 1/2 days?
Answer:
252 hours
Step-by-step explanation:
1 day = 24 hours
1 week = 7 days
= 24 * 7
= 168 hours
3 days = 24 * 3
= 72 hours
1/2 day = 24 / 2 = 12 hours
Add up all values/hours:
168 hours + 72 hours + 12 hours = 252 hours
Answer:
1 week- 168 hours
3 days-72 hours
1/2 day-12 hours
Step-by-step explanation:
1 week- 24x7=168
3 days- 24x3=72
1/2 day- 24x.5=12
find the missing angle measure in each figure
Answer:
x = 100°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 7, hence
sum = 180° × 5 = 900°
Sum the given interior angles and equate to 900
x + 155 + 116 + 135 + 135 + 116 + 143 = 900
x + 800 = 900 ( subtract 800 from both sides )
x = 100°
PLEASE HELP!! If the endpoints of have the coordinates A(9, 8) and B(-1, -2), what is the midpoint of ?
A. (5, 3)
B. (4, 5)
C.(5, 5)
D. (4, 3)
M refers to midpoint.
[tex]
A(9, 8) \\
B(-1, -2) \\
M(\frac{x_1-x_2}{2}, \frac{y_1-y_2}{2}) \\
M(\frac{9-(-1)}{2}, \frac{8-(-2)}{2}) \\
M(\frac{10}{2}, \frac{10}{2})\Longrightarrow\boxed{M(5, 5)}
[/tex]
Hope this helps.
r3t40
I need help with this
Answer: Angle 10 and Angle 2
How would you prove that ∠2 congruent ∠4?
Corresponding angles are congruent
From concept of base angle of parallel line, Option(D) Corresponding angles are congruent.
What is the concept to find the relation between ∠2 and ∠4 ?Given that ∠1 ≅ ∠2 .
In the diagram given aside, line a and b are parallel where the ∠4 and ∠2 are base angle subtended by the parallel lines.
From the traversal property of congruency, we know that the base angles of a parallel lines always subtend equal and congruent angles when it is intercepted by a common traversal.
Thus, from concept of base angle of parallel line, Option(D) Corresponding angles are congruent.
To learn more about base angle of parallel lines, refer -
https://brainly.com/question/13352230
#SPJ2
Help please ASAP !!!
For this case we have that by definition of trigonometric relations of rectangular triangles, that the sine of an angle is given by the opposite leg to the angle on the hypotenuse of the triangle. So:
[tex]Sin (45) = \frac {leg} {h}[/tex]
Where h is the hypotenuse.
[tex]\frac {\sqrt {2}} {2} = \frac {leg} {h}[/tex]
We cleared h:
[tex]h = \frac {2leg} {\sqrt {2}}[/tex]
We rationalize:
[tex]h = \frac {2leg} {\sqrt {2}} * \frac {\sqrt {2}} {\sqrt {2}}\\h = \frac {2 \sqrt {2} * leg} {2}\\h = \sqrt {2} * leg[/tex]
ANswer:
Option A
How far from the base of a building must the bottom of a 15-foot ladder sit in order for it to make a 52 angle with the ground? round to the nearest tenth of a foot.
Answer:
9.2 ft
Step-by-step explanation:
The length of the ladder is 15 ft
The ladder makes an angle of 52° with the ground
The distance (x) from the base of the house to the foot of the ladder is given by;
[tex]\frac{x}{15}[/tex] = cos 52°
x = 15 × cos 52° = 9.23492213 ft
Which equals to 9.2 ft (rounded off to tenth of a foot)
The distance between the base of the building and the bottom of the ladder is 11.72 feet.
It is given that
Length of the ladder = 15 feet
The angle of inclination = 52°
Let us say the distance between the base of the building and the bottom of the ladder is x.
What is the tangent of an angle?The tangent of an angle is the ratio of the opposite side(to that angle) to the base of the triangle.
Tan 52° = length of the ladder / distance between base of building and bottom of the ladder.
Tan 52 = 15/x
x= 15/Tan 52
x = 11.72 feet.
Therefore, The distance between the base of the building and the bottom of the ladder is 11.72 feet.
To get more about Trigonometric ratios visit:
https://brainly.com/question/24349828
find the equation of the circle that has a diameter with endpoints located at (-5 -3) and (-11 -3)
Answer: Option C
The equation is:
[tex](x+8)^2 +(y+3)^2=9[/tex]
Step-by-step explanation:
First we must calculate the midpoint between the two given points.
Then the midpoint will be the radius of the circumference
The midpoint between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is:
[tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
In this case the points are:
(-5 -3) and (-11 -3)
The the center is:
[tex](\frac{-5-11}{2}, \frac{-3-3}{2})[/tex]
[tex](-8,\ -3)[/tex]
Then the equation is:
[tex](x+8)^2 +(y+3)^2=r^2[/tex]
To find r we substitute one of the points in the equation and solve for r
[tex](-5+8)^2 +(-3+3)^2=r^2[/tex]
[tex](3)^2 +0=r^2[/tex]
[tex]r^2 =3^2[/tex]
[tex]r =3[/tex]
Finally the equation is:
[tex](x+8)^2 +(y+3)^2=9[/tex]
Answer:
Option C
Step-by-step explanation:
The standard form of equation of circle is:
(x-h)^2+ (y-k)^2=r^2
As we only know two points on the circle which are the ends of diameter.
As we know
Radius=Diameter/2
We have to find the length of diameter using the distance formula first to calculate radius. So,
Diameter= √((-11-(+5))^2+(-3-(-3)^2 )
= √((-11+5)^2+(-3+3)^2 )
=√((-6)^2+(0)^2 )
= √36
=6
Now,
Radius=6/2
=3
As the diameter passes through centre, so the mid-point of diameter will be centre of the circle:
Mid-point=((x_1+x_2)/2,(y_1+y_2)/2)
=((-5-11)/2,(-3-3)/2)
=((-16)/2,(-6)/2)
=(-8,-3)
Putting the values of radius and centre in standard form
(x-h)^2+ (y-k)^2=r^2
(x-(-8))^2+ (y-(-3))^2=3^2
(x+8)^2+ (y+3)^2=9
So the correct answer is option C ..
What number should be added to both sides of the equation to complete the square?
x2 – 6x = 5
I think 9 should be added to both sides.
cofficient of x = 6
half of it = 6/2 = 3
square the 3
to give 3 squared = 3*3 9
Answer:
9
Step-by-step explanation:
To make it a Perfect Square Trinomial, you can square root 9 and multiply it to get 6, therefore 9 is correct
c/3 = 30/5 what steps do I take to see what c is?
For this case we must find the value of "c" of the following expression:
[tex]\frac {c} {3} = \frac {30} {5}[/tex]
We solve the right side of the equation:
[tex]\frac {30} {5} = 6[/tex]
Rewriting:
[tex]\frac {c} {3} = 6[/tex]
We multiply both sides of the equation by "3":
[tex]c = 6 * 3\\c = 18[/tex]
Answer:
[tex]c = 18[/tex]
what is the measure of major arc MBD
Answer:
The measure of the major arc MBD is 270°
Step-by-step explanation:
we know that
The measure of major arc MBD is equal to the sum of the measure of the arc MB plus the measure of the arc BD
BD is a diameter-----> divide the circle into two equal parts
so
arc BD=180°
arc MB is a quarter of circle
so
arc MB=90°
therefore
arc MBD=180°+90°=270°
Annie had 7 apples, she sold 5 of them, and bought 3 more apples. Annie gave 2 apples to her friends, and then lucy gave her 9 apples, annie ate 6 apples, and found 89 more apples. How many apples does annie have now?
Answer:
Annie has 95 apples now
Answer:
Annie has 95 Apples
Step-by-step explanation:
7 Apples - 5 Apples = 2
2 + 3 more apples = 5 Apples
5 Apples - 2 Apples = 3 Apples
3 Apples + 9 more apples = 12 Apples
12 - 6 = 6 Apples
6 Apples + 89 more apples = 95 Apples
CAN SOMEONE PLEASE HELP ME ANSWER THIS
Answer:
12
Step-by-step explanation:
3•4=12
x-2y+3z=-2
6x+2y+z=-48
x+4y+3z=-38
Answer:
x = -94/17, y = -6, z = -48/17
Step-by-step explanation:
If solving this system of equations is what you want, here's the answer.
which inequality is equalivalent to |x-4|<9
Answer:
-5 < x < 13Step-by-step explanation:
[tex]|x-4|<9\iff x-4<9\ \wedge\ x-4>-9\qquad\text{add 4 to both sides}\\\\x<13\ \wedge\ x>-5\to-5<x<13[/tex]
The length of the hypotenuse of a 45°-45°-90° triangle is 22. Find the length of one leg.
Check the picture below.
Ari’s teacher says he may have his report grade based on either the mean or the median of his last six test scores.
88%, 73%, 97%, 76%, 90%, 80%
Which measure of center would best represent Ari’s grade?
Answer:
Mean because it is the average of all of them combined = best representation of all grades.
84% & Mean
Step-by-step explanation:
88 + 73 + 97 + 76 + 90 + 80 = 504
**divide by how many grades there are** (6 of them)
504 / 6 = 84
Meaning the best center representation would be 84%
Answer: The Mean
The mean is when you add up all of those grades and divide by the amount of exams.
At a local pizza place, the cost of a large cheese pizza is $13.99. Each additional topping is $1.25. The Tigerd family orders a large pizza topped with pepperoni, mushrooms, olives, and sausage. How much did their pizza cost?
Answer:
$18.99
Step-by-step explanation:
Step 1: Take the per topping amount ($1.25) and multiply it by the amount of toppings (4). $1.25x4=$5
Step 2: Add your toppings total ($5) to the base pizza cost ($13.99). $13.99+$5=$18.99
Answer:
18.99
work:
13.99 + (1.25 x 4 )
13.99 + 5
18.99
trust me, 18.99 + (1.25 x 4) will work and the work showing also
Mr. Grocer has 421 dozen eggs valued at $0.59 per dozen. How much are the eggs worth altogether?
248.39
713.56
420.41
421.59
Answer:
248.39
Step-by-step explanation:
421 × .59 =248.39
Can someone help with this plz?
Answer:
Hey No worries. Its very easy.
Step-by-step explanation:
Look,
Volume= 84 in.cube
Length=6 in.
Breadth=2 in.
therefore, Height= Volume/(Length*Breadth)
=84/(6*2)
=84/12
=7
Answer:
h = 7 in
Step-by-step explanation:
The volume (V) of a cuboid is calculated using the formula
V = lbh ( l is length, b is breadth and h is height )
Given V = 84 in³, then
lbh = 84 ← substitute l = 6 and b = 2
6 × 2 × h = 84
12h = 84 ( divide both sides by 12 )
h = 7
This question is very confusing for me can someone please help me
Essentially this question is asking, If we made circle O as big as circle O1, how could we move it to the same spot. Therefore, I would expect the Answer to be D.
Answer Numbers 5-8 with work
Answer: -3
Step-by-step explanation:8-5=3 take the negative so it’s -3
Let me know the answer plz
Answer: Option G
[tex]a_6 = -2048[/tex]
Step-by-step explanation:
The geometric series have the following form:
[tex]a_n = a_1 (r) ^ {n-1}[/tex]
Where [tex]a_1[/tex] is the first term of the sequence and r is the common radius.
In this case we know that
[tex]a_1 = -2\\\\r = 4[/tex]
So:
[tex]a_n = -2(4) ^ {n-1}[/tex]
To find the sixth term [tex]a_6[/tex], substitute [tex]n = 6[/tex] in the equation.
[tex]a_6 = -2 (4) ^ {6-1}\\\\a_6 = -2 (4) ^ 5\\\\a_6 = -2048[/tex]
Rationalize the denominator and simplify. StartFraction 5 minus StartRoot 3 EndRoot Over 4 plus 2 StartRoot 3 EndRoot EndFraction
Answer:
[tex]\frac{13-7\sqrt{3}}{2}[/tex]
Step-by-step explanation:
We need to rationalize the denominator of [tex]= \frac{5-\sqrt{3}}{4+2\sqrt{3}}[/tex]. For rationalizing we multiply the equation by [tex]\frac{4-2\sqrt{3}}{4-2\sqrt{3}}[/tex]
So, solving
[tex]= \frac{5-\sqrt{3}}{4+2\sqrt{3}}*\frac{4-2\sqrt{3}}{4-2\sqrt{3}} \\=\frac{(5-\sqrt{3})(4-2\sqrt{3})}{4+2\sqrt{3}*4-2\sqrt{3}}\\=\frac{(5-\sqrt{3})(4-2\sqrt{3})}{(4)^2-(2\sqrt{3})^2}\\= \frac{5(4-2\sqrt{3})-\sqrt{3}(4-2\sqrt{3})}{16-(4*3)}\\=\frac{20-10\sqrt{3}-4\sqrt{3}+2*3}{16-12}\\=\frac{20+6-14\sqrt{3}}{4}\\=\frac{26-14\sqrt{3}}{4}\\= \frac{2(13-7\sqrt{3})}{4}\\=\frac{13-7\sqrt{3}}{2}[/tex]
Answer:
0.25
Step-by-step explanation:
estimate the quotient 722 divided by 9
Answer: 72
Step-by-step explanation:
722 —> 720
9 —> 10
72 divided by 1 is 72
Help me!!! I am so confused
Answer:
[tex]\boxed{x^{2} + 2x - 8}[/tex]
Step-by-step explanation:
6. Practice
The dimensions of the current park are x long and x wide.
The new park will be 4 longer and 2 thinner.
Its new dimensions will be x + 4 long and x – 2 wide.
Its new area will be
A = width × length = (x – 2)(x + 4)
Find the product
[tex]\begin{array}{lll}\textbf{Steps} & \textbf{Problem: }(x - 2)(x + 4) & \\\textbf{1. List variables} & a = x - 2 & \\ & b = x & \\ & c = 4 &\\\textbf{2. Distribute (x - 2)} & (x -2)(x + 4)\\ & = (x - 2)(x) + (x - 2)(4)\\\textbf{3. Distribute x and 4} & x^{2} -2x + 4x - 8\\\textbf{4. Combine like terms}& x^{2} + 2x - 8\\\end{array}\\\text{The area of the updated skatepark will be }\boxed{\mathbf{ x^{2} + 2x - 8}}[/tex]
The ratio of the lengths of an ellipse is 3:2. If it’s area is 150 cm2, what are the lengths of The major and minor semiaxes respectively?
Answer:
the length of major semiaxes a = 8.45 cm and minor semiaxes b= 5.63 cm.
Step-by-step explanation:
Area of ellipse = π*a*b
Let major semiaxes = a and minor semiaxes = b
then a:b = 3:2
a/b = 3/2
=> a = 3/2 b
Putting in the value of formula
150 = π * (3/2)b * b
150 = 3.14 * 1.5b * b
150= 4.71 b^2
150/4.71 = b^2
=> b^2 = 31.8
b= 5.63
a = 3/2 * b
a = 1.5 * 5.63
a = 8.45
So, the length of major semiaxes a = 8.45 cm and minor semiaxes b= 5.63 cm.
Answer:
Major: 8.5 cm
Minor: 5.6 cm
Step-by-step explanation:
Please help I'm very confused
Answer: OCTOBER 16th
Step-by-step explanation: The teams will meet again on October 16th
What is the algebraic expression for the difference between seven times a number and three times that number"?
7 -3x
7x-3
7x-3x
Answer:
the last one
Step-by-step explanation:
Answer:
the answer is indeed the last one
Step-by-step explanation:
7x-3x is the only one that meets the requirements for this statement
7-3x would be the difference between seven and three times a number
7x-3 would be the difference between seven times a number and three
have an absolutely fantastic day my friend!
Jeremy is recording the weights, in ounces, of different rock samples in a lab. The weights of seven rocks are listed below.
11, 13, 14, 6, 10, 9, 10
The eighth rock that he weighed was 5 ounces. How would the interquartile range of the data be affected if Jeremy includes the weight of the eighth rock?
Answer:
The correct answer is option "C"
"The interquartile range increases"
The value of the (RIC) will increase from 4 to 5.75, that is, 44%
Step-by-step explanation:
The range is defined as the difference between the maximum and minimum value of a series of data. Xmax - Xmin
The interleaving range (RIC) is a measure of dispersion that measures the central range of 50% of the data.
Therefore, if a low value is included, such as five, the variance of the data would be greater and, consequently, the value of the (RIC) will increase from 4 to 5.75, that is, 44%